By combining ultrahigh energy resolution (~20 meV), high spatial resolution (~1 nm), and momentum resolution (~3 nm-1) in STEM–EELS, we can investigate physical properties over a broad spectral range from the ultraviolet to the infrared at the nanometer scale. For lattice vibrations (phonons), which play a key role in determining the thermal properties of materials, we have demonstrated (1) momentum-resolved measurements of phonon dispersions, (2) mapping of phonon intensities and vibrational modes, (3) detection of vibrational modes localized at interfaces, and (4) absolute temperature measurements based on phonon spectroscopy. For point defects, which strongly influence the optical and electronic properties of materials, we have investigated quantum emission centers and demonstrated (5) measurements of subgap electronic states and (6) visualization of point-defect concentration distributions. These advanced spectroscopic techniques are expected to contribute to nanoscale thermal management in power devices and to the research and development of quantum materials and quantum light-emitting materials. We are also developing spectroscopic techniques for probing the electronic states of organic materials, which have traditionally been difficult to investigate by electron microscopy because of electron-beam-induced damage. Low-dose measurements combined with low-noise, high-sensitivity detection enable us to extend STEM–EELS spectroscopy to these electron-beam-sensitive materials.